Assassin's Creed 2 is a big step up from Assassin's Creed 1. Almost everything is upgraded. The character models are improved, you have a few new weapons added to your arsenal, shops, an income system, etc. By far the biggest improvement, however, is the mission structure. The repetitive model of the first game is done away with, with your missions now consisting of more varied tasks than merely pickpocketing, eavesdropping and interrogating.
The GotY edition is definitely the version to get since with it you get the complete story, whereas without the added content there is just a gap in the storyline that is left unexplained. The additional content may not add much length overall but the two chapters are fun to play nonetheless.
One thing to note, however. Despite it being clearly advertised, the Templar Lairs are NOT included. I don't know whether it was just a programming error or they just weren't added in but they are not accessible at any point in the game. Ubisoft support appears to be playing dumb on this issue and do not seem to be giving an answer so I would not hold my breath for a fix, especially given that Assassin's Creed: Brotherhood has been released.
Overall, if you liked AC1 then you'll LOVE AC2.